What kind of responses will come back from an editor after a short story is accepted in an anthology? Specifically, is it common for a writer to hear that an accepted story has potential but needs significant editing before it's finally accepted? I've had a hard time finding any actual verbatim responses online.

I think it depends on the anthology/editor/publisher?
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TannaleinJul 3 '13 at 18:53

Sure, I understand that. I'm really looking for examples, and having a hard time tracking any down. My apologies for the somewhat vague and wide-reaching nature of the question.
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Scotch FenderJul 4 '13 at 0:15

Well, I don't have experience with English speaking ones, but the one I send my stories to just changed their MO this year. Previous years they would inform you by email if you got in, ask for a short bio and publish the story as is, but this year they said they will get back to the authors whose stories might be improved (which would have simply been rejected in previous years) and generally work with all authors on improving their stories. I hear some others in my country also work in this way. Raises the quality of the stories.
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TannaleinJul 4 '13 at 2:59

I don't know about for short stories, but in my one experience with a poem being published in an anthology, I just got one or two line edits back for slight grammatical mistakes I had made.
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kuwalyJul 24 '13 at 16:27

By and large, if you're sending a work to someone like a literary review magazine or an anthology in hopes it will be published, you must assume that they will only accept your work if it's 100% ready for publication. For one thing, the editors at these places simply do not have the time to engage in lengthy correspondence with 10 or 15 writers to help them polish their work up. For another, it's my experience, particular among beginning writers, that when you reach the point where you think a work is around 90% finished, it is in fact around 20% finished.

Just to give one an idea of the kind of polished manuscript editors expect, Ernest Hemingway used to say that he didn't feel that he even really understood a story until he'd rewritten it for around the 9th time or so, and he'd generally have a story undergo revisions well into the double digits. I'm not saying that you have to rewrite a story 10 times any time you get it published - everyone's process is different - but if it even looks like a rough draft, you are literally competing against people who have taken Hemingway to heart, and you will be judged harshly for that.

Finally, one should note that from an editor's standpoint, even if a story seems like it's almost there, there is a very good chance that the author simply is not going to agree with whatever changes the editor would like to make to the story. You aren't (necessarily) developing a long-term relationship with an editor here the way you would with a full-fledged novel (which can be a lot sloppier than a short story nowadays anyway). You're trying to get someone who is probably not getting paid a whole lot to see your vision in the 15 minutes it takes them to read your story. You simply can't afford to put out anything but the best possible version of the story you're writing.